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Simplifying b(15 + -3b)(15 + 5b) = 0 Multiply (15 + -3b) * (15 + 5b) b(15(15 + 5b) + -3b * (15 + 5b)) = 0 b((15 * 15 + 5b * 15) + -3b * (15 + 5b)) = 0 b((225 + 75b) + -3b * (15 + 5b)) = 0 b(225 + 75b + (15 * -3b + 5b * -3b)) = 0 b(225 + 75b + (-45b + -15b2)) = 0 Combine like terms: 75b + -45b = 30b b(225 + 30b + -15b2) = 0 (225 * b + 30b * b + -15b2 * b) = 0 (225b + 30b2 + -15b3) = 0 Solving 225b + 30b2 + -15b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '15b'. 15b(15 + 2b + -1b2) = 0 Factor a trinomial. 15b((5 + -1b)(3 + b)) = 0 Ignore the factor 15.Subproblem 1
Set the factor 'b' equal to zero and attempt to solve: Simplifying b = 0 Solving b = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b = 0Subproblem 2
Set the factor '(5 + -1b)' equal to zero and attempt to solve: Simplifying 5 + -1b = 0 Solving 5 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1b = 0 + -5 -1b = 0 + -5 Combine like terms: 0 + -5 = -5 -1b = -5 Divide each side by '-1'. b = 5 Simplifying b = 5Subproblem 3
Set the factor '(3 + b)' equal to zero and attempt to solve: Simplifying 3 + b = 0 Solving 3 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + b = 0 + -3 b = 0 + -3 Combine like terms: 0 + -3 = -3 b = -3 Simplifying b = -3Solution
b = {0, 5, -3}
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